Is this possible? The panel doesn't need to get the batteries anywhere close to fully charged, rather, it only needs to supplement their charge (these batteries are going to be part of a portable USB charger.

Of course it's possible. I use the LT1510 for many of my SA projects requiring NiMH batteries. That solar array is probably perfect. 250mA is adequate out of your SA. You'll need two of them to charge using the LT1510 though. The 1510 is a buck converter so if your input voltage is below your battery current it won't work properly. A buck-boost converter would probably be better for your application if you just want one SA panel, but 1.5W panel is adequate.

NiMH should be current controlled until the voltage starts falling, then it should stop charging. A secondary means of stopping charging should be implemented, as well, this is usually done with a temperature threshold on a NiMH cell.